Title: Homogenization of active suspensions and reduction of effective viscosity Show Chinese title

Title: 活性悬浮液的均匀化与有效黏度的降低

Abstract: We consider a suspension of active rigid particles (swimmers) in a steady Stokes flow, where particles are distributed according to a stationary ergodic random process, and we study its homogenization in the macroscopic limit. A key point in the model is that swimmers are allowed to adapt their propulsion to the surrounding fluid deformation: swimming forces are not prescribed a priori, but are rather obtained through the retroaction of the fluid. Qualitative homogenization of this nonlinear model requires an unusual proof that crucially relies on a semi-quantitative two-scale analysis. After introducing new correctors that accurately capture spatial oscillations created by swimming forces, we identify the contribution of the activity to the effective viscosity. In agreement with the physics literature, an analysis in the dilute regime shows that the activity of the particles can either increase or decrease the effective viscosity (depending on the swimming mechanism), which differs from the well-known case of passive suspensions. Show Chinese abstract

Abstract: 我们研究了一种活性刚性粒子（游泳者）悬浮液在稳态斯托克斯流中的情况，其中粒子根据平稳遍历的随机过程分布，并研究了其在宏观极限下的均匀化。模型的关键点在于允许游泳者根据周围流体变形调整它们的推进力：游泳力不是事先规定的，而是通过流体的反馈获得的。对该非线性模型进行定性均匀化需要一种非常规的证明，该证明关键依赖于半定量的双尺度分析。在引入新的校正项以准确捕捉由游泳力产生的空间振荡后，我们确定了活动性对有效粘度的贡献。与物理学文献一致，在稀疏极限下的分析表明，颗粒的活动性可以增加或减少有效粘度（这取决于游泳机制），这与众所周知的被动悬浮液的情况不同。